limit cycles

The existence of limit cycles for a class of planar quadratic equations

一类平面二次方程的极限环存在性

On the number and distributions of limit cycles in a cubic system

一类三次系统极限环的个数与分布

An Algorithm of Stability and Bifurcation of Limit Cycles for Cubic System

三次系统极限环及其稳定和分岔的一种算法

Qualitative Analysis to A Class of Prey-Predator System with Holling's Type ⅱ Functional Response and Having Two Limit Cycles

一类具HOllingⅡ类功能性反应且存在两个极限环的捕食系统的定性分析

An indirect method is used to study bifurcations of limit cycles at infinity for a class of seventh-order polynomial differential system.

运用一种间接的方法研究了一类七次系统在无穷远点的中心条件和极限环分支问题。

The Number of Limit Cycles for Certain Two-Dimensional Systems

一类二维系统的极限环的个数

In the paper [ 1], a equation E α,β of biochemical reaction was established and some numeral computations for the limit cycles were obtained.

文[1]建立了一类生化反应方程E（α，β），该文借助于计算机作了极限环的一些数值计算。

The purpose of this paper is to discuss the existence and uniqueness of limit cycles for a class of plane n degree system with the origin being a stellar node.

本文讨论了原点是星形结点的一类平面n次系统的极限环的存在性和唯一性，并给出一类平面三次系统的极限环分支曲线。

Limit Cycles of a Cubic System with Two Tangent Circle Solutions

具有两个相切圆解的三次系统的极限环

Bifurcation of limit cycles forming compound eyes in a planar cubic differential system(ⅱ)

平面三次微分系统的极限环复眼分枝（Ⅱ）

This paper discusses correspondence between homogeneous polynomial vector field of even degree Q ( x) in R3 and the induced tangent vector field QT ( x) of Q ( x) on S2 and some geometric properties of solutions. The nonexistence of limit cycles is proved.

本文讨论了偶次多项式齐次向量场和S2上的导出切向量场之间的对应关系和轨迹的一些几何性质，并证明了Q（X）不存在极限环。

Uniqueness of a class of limit cycles surrounding multiple singular points

一类包围多奇点极限环的唯一性

Examples of one double limit cycle or two single limit cycles jumping from an infinite Separatrix Cycle in a quadratic system

二次系统的二重极限环和以无限大分界线环分支出两个极限环的例子

Stability of limit cycles and the divergence of its vector field

极限环的稳定性和对应矢量场的散度

Uniqueness of Limit Cycles of the Second Order Polynomial Autonomous System

二阶n次多项式自治系统的极限环的唯一性

In this article, the center conditions, isochronous center conditions and bifurcation of limit cycles at infinity for a class of fifth system are investigated.

研究一类五次系统无穷远点的中心、拟等时中心条件与极限环分支问题。

Hilbert' 16th problem is to determine the minimum upper bound for the number of limit cycles of plane vector fields, and their relative location.

D.Hilbert在1900年展望20世纪数学的未来时，提出的著名的23个数学问题的第16个问题，就是寻求平面向量场极限环个数的最小上界，以及这些极限环可能出现的相对位置。

The bifurcation of limit cycles at infinity for a class of cubic polynomial systems was studied in the paper.

研究了一类三次系统无穷远点的极限环分支问题。

A geometric criterion for monotonically-approached semi-stable limit cycles is given, which enables one to draw the limit cycles, Conditions of stability are established for space limit cycles and equilibrium points of second order nonautonomous systems.

对单调接近的半稳定极限环给出了一个几何条件，按此条件可以作图画出这种极限环。还对空间极限环和二阶非自治系统平衡位置各得到一个稳定性条件。

By the control of parameter conditions and using the method of detection functions, the facts of there exist 20-23 limit cycles forming different compound eyes can be proved.

通过控制参数，利用判定函数的方法，证明系统存在20&23个极限环，形成不同的复眼分布。